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There are a couple of ways to analyze suspension bridges. As previously discussed (Uniqueness and Difficulties of Suspension Bridge Analysis), the deflection theory proposed by Melan and solved by Moisseiff is one of the first. The second one may be trigonometric methods proposed by Timoshenko (Theory of suspension bridges, Journal of the Franklin Institute, Volume 235, Issue 4, April 1943, Pages 327-349). In this article, a brief explanation of trigonometric methods and related excel, and the example bridge dimensions will be provided.
What is the Equilibrium Equation for Dynamic Problems?
The equilibrium equation for any dynamic problem can be expressed as Eq (1).Eq (1) is just an extension of a more familiar equilibrium equation for a static problem.In Eq (2), F is the applied force, k is the stiffness, and y is the displacement. We know F and K, so we can calculate y. In other words, we have only one unknown y, so we can calculate y.
With the help of Tarcisio Barreto Celestino and Antonio Bobet, our MIDAS Expert Osvaldo Paiva Magalhães Vitali took on a new approach using midas GTS NX on tunnels with complex ground and loading conditions. In their recent publication in the Soils and Rocks Journal, we can see how they used the features in midas GTS NX to impose body forces to the 3D finite elements; this is done by providing components of the Cauchy stress tensor.
What is Bridge Redundancy?
Bridge redundancy is the capacity of the structure to carry loads after the structure is damaged or after one of its members ruptures. The manual for Bridge Evaluation (2008) defines bridge redundancy as the “capacity of the bridge to carry loads after damage or the failure of one or more of its members”.
How to Perform Time-dependent Analysis?
Mainly there are two ways to perform the time-dependent analysis. One is the time-step analysis and the other is the age-adjusted method. The age-adjusted method is a simplified one and can consider the long-term effects with only a one-step analysis. Of course, this is an approximate way to consider...
In the blog article intro to Time-dependent Analysis for Concrete Structures, we have touched upon the importance of construction stage analysis for concrete structures. The material time function can be plotted and inputted into analysis software like midas Civil to simulate their changing material behavior in various stages of the construction. This article will go over the process of calculating various parameters that contribute to the shape and location of the material's time functions.
In the article "strut-and-tie modeling for pier caps", we have discussed the definition of strut-and-tie analysis and how to construct a strut-and-tie model using the example of pier cap. After creating the geometry of a strut-and-tie model, the next step usually is calculating dead and live loads from the superstructure. This article discusses how to determine the boundary loads for a pier cap with a superstructure that has irregular geometries.
Before starting the rigorous discussion about time-dependent analysis, let's start a simple structural analysis problem.
What is the reaction R1 for the blow fixed end beam?
What is Strut-and-Tie Analysis? What are "Struts" and "Ties" in Struct-and-Tie Analysis?
Struct-and-tie analysis visualizes the flow of forces through any type of concrete element in the form of internal truss. The tensile members of the internal truss are called "ties" and the compressive members of the internal truss are called "struts" in struct-and-tie analysis. The joints that are needed to join the two types of members together are called "nodes"
What is Convergence? What is Convergence Study?
It is easy to obtain the result from bridge finite element analysis, but to get more accurate results requires extra efforts. Even the most robust finite element analysis solvers adopts the method that approximates the structural behavior, by minimizing the associated error function compared with...
How to Model the Girder and Deck Connection in Composite Bridge?
The way to simulate the connection between the girder and the deck will depend on how we construct the model. In the 2D all-frame composite bridge model shown in figure 1, all the elements are connected in the grid within the same plane. Because it was modeled with...
Why is cable-stayed bridge difficult to analyze? Cable-stayed bridges, including so-called Extradosed bridges, do not have any classical solutions. Computer based displacement method is the only way to analyze cable-stayed bridges and it is hard to check the output. Also, in the cable-stayed bridge analysis, the following three nonlinearities should be considered.
Bridge load posting – identifying just how much weight a bridge can bear – is a matter of public safety and a way to safeguard vital transportation infrastructure. However, load posting is less straightforward than it may seem. Not posting a bridge can create safety issues for the motoring public, while posting makes transportation more difficult for large, heavy vehicles and the industries that use them.
In this article, Dr. Lee shows the stiffness strengthening effects caused by tension in the cantilever beam, and demonstrates through example how that contributes to one of the key concepts in the suspension bridge analysis.
From the previous tip basic nonlinear analysis explained, Dr. Seungwoo Lee talked about some fundamental differences between linear and nonlinear analysis in structural engineering. In a linear analysis, the relationship between the stress and strain of a model is held constantly, and the stiffness matrix of the model stays the same throughout the analysis.
When we talk about prestressed concrete, the things that we are mostly concerned about are the compressive strength gain with respect to time, and the prestressing tendon relaxation with respect to time. Figure 1 shows various time-dependent effects for concrete including creep and shrinkage. The factors that affect the creep rate include water/cement ratio, age and strength of the concrete when it is subjected to stress, and ambient temperature and humidity.
A linear analysis is when a linear relationship is held constantly for the stress and strain of a model, meaning that the stiffness matrix of the model stays the same throughout the analysis. However, when can an analysis be called non-linear? What are the types of non-linear analysis? Seungwoo Lee, Ph.D., senior supervising engineer at WSP USA is here with us to talk about some basic types of non-linear analysis.
For structures with stability issues, one way to check which specific link is causing the problem is start with a constrained model and begin relaxing its DOFs gradually. When you are releasing the DOFs and when you are running into stability issues, you would know which link release is causing that instability.
This piece of tip talks about different types of links that you can find in midas Civil and their applications. You may be wondering what are the implications of using one type of link compared to another, this tip will answer that for you and help you gain more confidence when choosing the link types.
In the design project to replace the old Fulton Road arch bridge in Cleveland, OH, Michael Baker Intl engineer Daniel Baxter and his team has designed a 1,568-foot-long replacement structure for the original arch bridge, which retains the original design of six 210-foot-long concrete deck arch spans. For the replacement bridge structure, a precast, post-tensioned concrete arch bridge design was selected. You may be asking yourself, why post-tensioning the arch bridge?
In typical engineering practices, engineers are used to having six degrees of freedom (DOFs) for modeling and analysis, three for rotations and three for translation. However, additional advanced beam elements can include other DOFs to represent the warping of an open thin-walled cross section. Such elements are not commonly available in professional software.
There are times when engineers would have to design and evaluate bridge structures that fall outside of the AASHTO design guideline. Therefore, when do we define a structure as irregular? How is evaluating an irregular bridge different from evaluating a regular bridge? How to minimize errors during the construction of irregular bridges?
Our Midas Civil software is versatile and very compatible with other software and Excel. This feature really useful to help engineers work faster on their project. Our Expert Engineer Seth Greenberg from Jacobs shared his tips to work faster with Midas Civil.
Midas Civil has so many features that can help you to work efficiently in your project. Our Expert Engineer Benjamin Blasen from Jacobs shared his quick tips in Midas Civil. The tips/tricks he has found very useful are the Query tools, using the MCT command shell, and turning on the display of frame and plane thicknesses in the Hidden Option Display menu.
There are so many ways to help you save your time when you are working on your bridge project. One of the easy tips is renumbering of the nodes and elements. Our Expert Engineer Tom Less, P.E., a Senior Associate, Team Leader & Bridge/Structural Engineer from Woolpert shared his tips for nodes and elements.
A complex bridge is one of the most common engineering projects nowadays. This category of structures includes movable, cable-stayed, segmental concrete, and other bridges with unusual characteristics. These types of structures will require specialized expertise to design and build. One of our Expert Engineers, Yazeed Abuhassan, a Structural Design Engineer from Bergmann PC, shared his tips about designing a complex bridge.
In this session, Yong Yang, principal structural engineer from Jacobs, will be demonstrating how plastic hinges can be set up quickly by the automatic determination of cross-sectional properties and member material through midas Civil's general section design (GSD) module.
Believe it or not, once upon a time, there were no computers available for us, bridge engineers. At that time, we had to perform every calculation by hand using calculators or even slide-rules. It was quite dull and time-consuming. Now all we have cutting-edge computers, which is way better than those we used when we landed at the Moon. Everything looks nice, and life seems beautiful, doesn't it?